Mathematical modeling of hot isotatic pressing of tubes from powder materials

Objectives . The work set out to create a mathematical model to investigate the process of hot isostatic pressing (HIP) process of long tubes from powder materials in metal capsules. By analyzing the stress-strain state in the areas far from the top and bottom borders in the cylindrical system of coordinates, the axial strain rate at every moment of the process can be considered to be constant through the entire volume. Methods . Mathematical modeling methods were used to describe mechanical properties in the process of HIP deformation by Green’s model of porous compressible media. The HIP capsule material, which is considered to be non-compressible, is described by the ideal plasticity model. The temperature field is assumed to be uniform over the volume and constant during the time of deformation. Results . The hypothesis of the uniform density over the cross section at each moment of the process was considered during analysis to the extent that the wall thickness of the tube is substantially less than its diameter. This hypothesis allowed us to reduce the task of determining the strain rates at every step of the process to a solution comprising two equations having two variables. When the strain rates are determined, the deformation field is built to obtain the final dimensions of the tube when the powder material is fully consolidated at the end of the HIP process. Conclusions . The proposed model for describing the process hot isostatic pressing of long tubes from powder materials takes all the features of this process into account depending on the system parameters. The possibility of using tubular samples to determine the functions included in the Green’s condition is demonstrated.